Question

In how many ways can 5 different books be arranged on a shelf if 2 books are never together

Answer 1

Since 2 books are never together, we can arrange these two books at 4 places (2 places in between the remaining 3 books + 2 at the ends) in ⁴P₂ ways.

After this the remaining 3 books can be arranged in ³P₃ ways.

Hence, the total number of arrangements in which 2 books are never together

= ⁴P₂ × ³P₃

= `(4!)/(2!) xx 3!`

= `(4 xx 3 xx 2 xx 1)/(2!) xx 3 xx 2!`

= 72.